cvpr maths -- 2

i want the below questions answered:
We aim to create a 3D point-cloud from three different views of a scene. The following
question will address the various steps involved in generating 3D from three views of the
scene.
1st: Let’s consider affine transformations, which are any transformations that preserve
parallelism. Affine transformations include not only rotations and translations, but
also scaling and shearing. Given some vector p, an affine transformation is defined
as: A(p) = Mp + b, where M is an invertible matrix. Prove that under any affine
transformation, the ratio of parallel line segments is invariant, but the ratio of nonparallel line segments is not invariant
2nd: We want to calibrate the intrinsic parameters of all the 4 cameras. Describe a way
to calculate the intrinsic parameters of the camera. Provide a derivation to estimate
the intrinsic parameters for one camera.
3rd: Explain the stages involved in creating a 3D point cloud from these four views –
give a 3-4 line description for each stage along with the equations.
4th: Write a derivation of estimating Fundamental matrix from 8 corresponding points
for a pair of views.
5th:Explain how will you use the Fundamental matrix F and the Intrinsic parameters
of each of the cameras to enforce Epipolar constraints to refine the correspondences
to obtain the 3D point cloud.
6th: Now you have the 3D scene point cloud and you have obtained a new image of
the scene with known intrinsic calibration. How will you establish correspondences
between the 3D point cloud and the new 2D image of the scene.